The Philosophy of Quantum Theory

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Quantum Mechanics A
Schrödinger Equation
The most fundamental equation of quantum mechanics; given a Hamiltonian \mathcal{H}, it describes how a state |\Psi\rangle evolves in time.
Basic Concepts and Theory of Motion
UV Catastrophe (Black-Body Radiation)
Photoelectric Effect
Stability of Matter
Double Slit Experiment
Stern-Gerlach Experiment
The Principle of Complementarity
The Correspondence Principle
The Philosophy of Quantum Theory
Brief Derivation of Schrödinger Equation
Relation Between the Wave Function and Probability Density
Stationary States
Heisenberg Uncertainty Principle
Some Consequences of the Uncertainty Principle
Linear Vector Spaces and Operators
Commutation Relations and Simultaneous Eigenvalues
The Schrödinger Equation in Dirac Notation
Transformations of Operators and Symmetry
Time Evolution of Expectation Values and Ehrenfest's Theorem
One-Dimensional Bound States
Oscillation Theorem
The Dirac Delta Function Potential
Scattering States, Transmission and Reflection
Motion in a Periodic Potential
Summary of One-Dimensional Systems
Harmonic Oscillator Spectrum and Eigenstates
Analytical Method for Solving the Simple Harmonic Oscillator
Coherent States
Charged Particles in an Electromagnetic Field
WKB Approximation
The Heisenberg Picture: Equations of Motion for Operators
The Interaction Picture
The Virial Theorem
Commutation Relations
Angular Momentum as a Generator of Rotations in 3D
Spherical Coordinates
Eigenvalue Quantization
Orbital Angular Momentum Eigenfunctions
General Formalism
Free Particle in Spherical Coordinates
Spherical Well
Isotropic Harmonic Oscillator
Hydrogen Atom
WKB in Spherical Coordinates
Feynman Path Integrals
The Free-Particle Propagator
Propagator for the Harmonic Oscillator
Differential Cross Section and the Green's Function Formulation of Scattering
Central Potential Scattering and Phase Shifts
Coulomb Potential Scattering

Although there is agreement by all physicists that quantum theory works in the sense that it predicts results that are in excellent agreement with experiment, there is a growing controversy over its philosophic foundation. Neils Bohr has been the principal architect of the present interpretation, known as the Copenhagen interpretation, of quantum mechanics. His approach is supported by the vast majority of theoretical physicist today. Nevertheless, a sizable body of physicists, not all in agreement with one another, questions the Copenhagen interpretation. The principal critic of this interpretation was Albert Einstein. The Einstein-Bohr debates are a fascinating part of the history of physics. Bohr felt that he had met every challenge that Einstein invented by way of thought experiments intended to refute the uncertainty principle. Einstein finally conceded the logical consistency of the theory and its agreement with the experimental facts, but he remained unconvinced to the end that it represented the ultimate physical reality. "God does not play dice with the universe," he said, referring to the abandonment of strict causality and individual events by quantum theory in favor of a fundamentally statistical interpretation.

Heisenberg stated the commonly accepted view succinctly: "We have not assumed that the quantum theory, as opposed to classical theory, is essentially a statistical theory, in the sense that only statistical conclusions can be drawn from exact data.... In the formulation of the causal law, namely, 'If we know the present exactly, we can predict the future,' it is not the conclusion, but rather the premise which is false. We cannot know, as a matter of principle, the present in all its details."

We should notice the acceptance of the correctness of quantum mechanics at the atomic and nuclear level. The search for a deeper level where quantum mechanics might be superseded is motivated much more by objection to its philosophic non-determinism than by other considerations. According to Einstein, "The belief in an external world independent of the perceiving subject is the basis of all natural science." Quantum mechanics, however, regards the interactions of object and observer as the ultimate reality. It uses the language of physical relations and processes rather than that of physical qualities and properties. It rejects as meaningless and useless the notion that behind the universe of our perception there lies a hidden objective world ruled by causality; instead it confines itself to the description of the relations among perceptions. Nevertheless, there is a reluctance by many to give up attributing objective properties to elementary particles, say, and dealing instead with our subjective knowledge of them, and this motivates their search for a new theory. According to de Broglie, such a search is in the interest of science. Whether it will lead to a new theory that in some currently unexplored realm contradicts quantum theory and also alters its philosophical foundations, no one knows.

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